BEIRUT, March 29 (Reuters) - Hezbollah leader Sayyed Hassan Nasrallah on Saturday called for domestic support for his militants after a year of growing sectarian violence in Lebanon following the Shi'ite militant group's intervention in the Syrian war.

"Some in Lebanon say the resistance (Hezbollah) has nothing to do with Syria," Nasrallah told supporters via a television link from a secret location in South Lebanon.

He justified sending his forces to a foreign war by saying that Sunni rebel groups would "eliminate everyone in Lebanon" if they won in Syria.

"The problem in Lebanon is not that Hezbollah went to Syria, but that we were late in doing so," he said. "This resistance will remain solid, with its head hung high, protecting its people and its nation."

Established nearly 30 years ago to confront Israel's occupation of south Lebanon, Hezbollah once won praise from Sunnis and Shi'ites across the Middle East. But its fight alongside Assad has lost it much domestic and international support.

Shi'ite Muslim Hezbollah fighters have helped turn the tide for Syrian President Bashar al-Assad in the military struggle against rebels. Assad now has a firm hold on much of central Syria around the capital and the Syrian-Lebanese border.

But the three-year-old conflict in Syria has fuelled Sunni-Shi'ite tensions in neighbouring Lebanon and across the wider Arab world. Syria's rebels are mostly Sunnis, while Assad belongs to the Alawite faith, an offshoot of Shi'ite Islam.

Syrian rebel groups and Lebanese supporters have carried out several suicide bombings in Hezbollah-controlled areas in Beirut and elsewhere, killing dozens of people. They have vowed to keep attacking Hezbollah until it withdraws its forces from Syria.

Nasrallah said he first sent "tens of Hezbollah" fighters to Syria to protect a Shi'ite shrine and "avoid larger sectarian strife". Since then, Hezbollah fighters in Syria have increased significantly but exact figures are not known.

Hezbollah and Assad share the same patron, Iran, which has supported the Syrian leader throughout the revolt. (Reporting by Oliver Holmes; Editing by Angus MacSwan)